Question

the supply function for manufacturing a certain item is p(x)=x^2+46x−66 { the demand function is p(x)=56x+30 if x represents the number of items (in hundreds), what is the optimum number of items to be manufactured?

Answer 1

optimal # of items occurs when supply = demand

so set x^2 + 46x - 66 = 56x + 30 and solve for x

then, since each x represents 100 items, you will then multiply the result by 100

let me know if you're having trouble or want to check your solution

welcome to QC!

Answer 2

im confused..

Answer 3

i did what you said i go a decimal....

Answer 4

hm.

x^2 + 46x - 66 = 56x + 30

start by combining like terms. first, subtract 56x from both sides.

Answer 5

i did

Answer 6

good

so x^2 - 10x - 66 = 30

now try subtracting 30 from each side

Answer 7

i thought you add 66 to both sides :(

Answer 8

but okay

Answer 9

you could add 66 if you wanted to, as long as all the terms end up on one side

adding 66 would give us

x^2 - 10x = 96

then you can subtract 96 from both sides to get

x^2 - 10x - 96

now, you will need to find two numbers that multiply to -96 and add up to -10

lmk if you need some help with this

Answer 10

-16+6

Answer 11

good so it factors to (x-16)(x+6) = 0

what is x equal to? keep in mind you only need to consider the positive x solution here

Answer 12

i dont even know... tbh

Answer 13

if you have A*B = 0 you know that either A = 0 or B = 0

so (x-16) = 0
(x+6) = 0

solve for x, you will get one positive and one negative value

Answer 14

-6+6=0 ; 16-16=0

Answer 15

good so

x - 16 = 0 means that x = 16
x + 6 = 0 means that x = -6

since x = the number of items, this cannot be negative so we only consider

x = 16

since each x represents 100 items, multiply this by 100 to get

1600 = your solution

Answer 16

thanks so much !